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Scale 2543: "Dydygic"

Scale 2543: Dydygic, Ian Ring Music Theory

Bracelet Diagram

The bracelet shows tones that are in this scale, starting from the top (12 o'clock), going clockwise in ascending semitones. The "i" icon marks imperfect tones that do not have a tone a fifth above. Dotted lines indicate axes of symmetry.

Tonnetz Diagram

Tonnetz diagrams are popular in Neo-Riemannian theory. Notes are arranged in a lattice where perfect 5th intervals are from left to right, major third are northeast, and major 6th intervals are northwest. Other directions are inverse of their opposite. This diagram helps to visualize common triads (they're triangles) and circle-of-fifth relationships (horizontal lines).

Common Names

Zeitler
Dydygic

Analysis

Cardinality

Cardinality is the count of how many pitches are in the scale.

9 (enneatonic)

Pitch Class Set

The tones in this scale, expressed as numbers from 0 to 11

{0,1,2,3,5,6,7,8,11}

Forte Number

A code assigned by theorist Allen Forte, for this pitch class set and all of its transpositional (rotation) and inversional (reflection) transformations.

9-5

Rotational Symmetry

Some scales have rotational symmetry, sometimes known as "limited transposition". If there are any rotational symmetries, these are the intervals of periodicity.

none

Reflection Axes

If a scale has an axis of reflective symmetry, then it can transform into itself by inversion. It also implies that the scale has Ridge Tones. Notably an axis of reflection can occur directly on a tone or half way between two tones.

none

Palindromicity

A palindromic scale has the same pattern of intervals both ascending and descending.

no

Chirality

A chiral scale can not be transformed into its inverse by rotation. If a scale is chiral, then it has an enantiomorph.

yes
enantiomorph: 3827

Hemitonia

A hemitone is two tones separated by a semitone interval. Hemitonia describes how many such hemitones exist.

7 (multihemitonic)

Cohemitonia

A cohemitone is an instance of two adjacent hemitones. Cohemitonia describes how many such cohemitones exist.

5 (multicohemitonic)

Imperfections

An imperfection is a tone which does not have a perfect fifth above it in the scale. This value is the quantity of imperfections in this scale.

2

Modes

Modes are the rotational transformations of this scale. This number does not include the scale itself, so the number is usually one less than its cardinality; unless there are rotational symmetries then there are even fewer modes.

8

Prime Form

Describes if this scale is in prime form, using the Rahn/Ring formula.

no
prime: 991

Deep Scale

A deep scale is one where the interval vector has 6 different digits.

no

Interval Formula

Defines the scale as the sequence of intervals between one tone and the next.

[1, 1, 1, 2, 1, 1, 1, 3, 1]

Interval Vector

Describes the intervallic content of the scale, read from left to right as the number of occurences of each interval size from semitone, up to six semitones.

<7, 6, 6, 6, 7, 4>

Interval Spectrum

The same as the Interval Vector, but expressed in a syntax used by Howard Hanson.

p7m6n6s6d7t4

Distribution Spectra

Describes the specific interval sizes that exist for each generic interval size. Each generic <g> has a spectrum {n,...}. The Spectrum Width is the difference between the highest and lowest values in each spectrum.

<1> = {1,2,3}
<2> = {2,3,4}
<3> = {3,4,5}
<4> = {4,5,6}
<5> = {6,7,8}
<6> = {7,8,9}
<7> = {8,9,10}
<8> = {9,10,11}

Spectra Variation

Determined by the Distribution Spectra; this is the sum of all spectrum widths divided by the scale cardinality.

1.778

Maximally Even

A scale is maximally even if the tones are optimally spaced apart from each other.

no

Maximal Area Set

A scale is a maximal area set if a polygon described by vertices dodecimetrically placed around a circle produces the maximal interior area for scales of the same cardinality. All maximally even sets have maximal area, but not all maximal area sets are maximally even.

no

Interior Area

Area of the polygon described by vertices placed for each tone of the scale dodecimetrically around a unit circle, ie a circle with radius of 1.

2.683

Polygon Perimeter

Perimeter of the polygon described by vertices placed for each tone of the scale dodecimetrically around a unit circle.

6.038

Myhill Property

A scale has Myhill Property if the Interval Spectra has exactly two specific intervals for every generic interval.

no

Balanced

A scale is balanced if the distribution of its tones would satisfy the "centrifuge problem", ie are placed such that it would balance on its centre point.

no

Ridge Tones

Ridge Tones are those that appear in all transpositions of a scale upon the members of that scale. Ridge Tones correspond directly with axes of reflective symmetry.

none

Propriety

Also known as Rothenberg Propriety, named after its inventor. Propriety describes whether every specific interval is uniquely mapped to a generic interval. A scale is either "Proper", "Strictly Proper", or "Improper".

Improper

Common Triads

These are the common triads (major, minor, augmented and diminished) that you can create from members of this scale.

* Pitches are shown with C as the root

Triad TypeTriad*Pitch ClassesDegreeEccentricityCloseness Centrality
Major TriadsC♯{1,5,8}242.64
G{7,11,2}342.21
G♯{8,0,3}342.14
B{11,3,6}342.21
Minor Triadscm{0,3,7}342.21
fm{5,8,0}342.36
g♯m{8,11,3}442.07
bm{11,2,6}342.29
Augmented TriadsD♯+{3,7,11}442
Diminished Triads{0,3,6}242.57
{2,5,8}242.71
{5,8,11}242.43
g♯°{8,11,2}242.43
{11,2,5}242.57
Parsimonious Voice Leading Between Common Triads of Scale 2543. Created by Ian Ring ©2019 cm cm c°->cm B B c°->B D#+ D#+ cm->D#+ G# G# cm->G# C# C# C#->d° fm fm C#->fm d°->b° Parsimonious Voice Leading Between Common Triads of Scale 2543. Created by Ian Ring ©2019 G D#+->G g#m g#m D#+->g#m D#+->B f°->fm f°->g#m fm->G# g#° g#° G->g#° bm bm G->bm g#°->g#m g#m->G# b°->bm bm->B

view full size

Above is a graph showing opportunities for parsimonious voice leading between triads*. Each line connects two triads that have two common tones, while the third tone changes by one generic scale step.

Diameter4
Radius4
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 2543 can be rotated to make 8 other scales. The 1st mode is itself.

2nd mode:
Scale 3319
Scale 3319: Tholygic, Ian Ring Music TheoryTholygic
3rd mode:
Scale 3707
Scale 3707: Rynygic, Ian Ring Music TheoryRynygic
4th mode:
Scale 3901
Scale 3901: Bycrygic, Ian Ring Music TheoryBycrygic
5th mode:
Scale 1999
Scale 1999: Zacrygic, Ian Ring Music TheoryZacrygic
6th mode:
Scale 3047
Scale 3047: Panygic, Ian Ring Music TheoryPanygic
7th mode:
Scale 3571
Scale 3571: Dyrygic, Ian Ring Music TheoryDyrygic
8th mode:
Scale 3833
Scale 3833: Dycrygic, Ian Ring Music TheoryDycrygic
9th mode:
Scale 991
Scale 991: Aeolygic, Ian Ring Music TheoryAeolygicThis is the prime mode

Prime

The prime form of this scale is Scale 991

Scale 991Scale 991: Aeolygic, Ian Ring Music TheoryAeolygic

Complement

The enneatonic modal family [2543, 3319, 3707, 3901, 1999, 3047, 3571, 3833, 991] (Forte: 9-5) is the complement of the tritonic modal family [67, 193, 2081] (Forte: 3-5)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2543 is 3827

Scale 3827Scale 3827: Bodygic, Ian Ring Music TheoryBodygic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2543 is chiral, and its enantiomorph is scale 3827

Scale 3827Scale 3827: Bodygic, Ian Ring Music TheoryBodygic

Transformations:

T0 2543  T0I 3827
T1 991  T1I 3559
T2 1982  T2I 3023
T3 3964  T3I 1951
T4 3833  T4I 3902
T5 3571  T5I 3709
T6 3047  T6I 3323
T7 1999  T7I 2551
T8 3998  T8I 1007
T9 3901  T9I 2014
T10 3707  T10I 4028
T11 3319  T11I 3961

Nearby Scales:

These are other scales that are similar to this one, created by adding a tone, removing a tone, or moving one note up or down a semitone.

Scale 2541Scale 2541: Algerian, Ian Ring Music TheoryAlgerian
Scale 2539Scale 2539: Half-Diminished Bebop, Ian Ring Music TheoryHalf-Diminished Bebop
Scale 2535Scale 2535: Messiaen Mode 4, Ian Ring Music TheoryMessiaen Mode 4
Scale 2551Scale 2551: Thocrygic, Ian Ring Music TheoryThocrygic
Scale 2559Scale 2559: Decatonic Chromatic 2, Ian Ring Music TheoryDecatonic Chromatic 2
Scale 2511Scale 2511: Aeroptyllic, Ian Ring Music TheoryAeroptyllic
Scale 2527Scale 2527: Phradygic, Ian Ring Music TheoryPhradygic
Scale 2479Scale 2479: Harmonic and Neapolitan Minor Mixed, Ian Ring Music TheoryHarmonic and Neapolitan Minor Mixed
Scale 2415Scale 2415: Lothyllic, Ian Ring Music TheoryLothyllic
Scale 2287Scale 2287: Lodyllic, Ian Ring Music TheoryLodyllic
Scale 2799Scale 2799: Epilygic, Ian Ring Music TheoryEpilygic
Scale 3055Scale 3055: Messiaen Mode 7, Ian Ring Music TheoryMessiaen Mode 7
Scale 3567Scale 3567: Epityllian, Ian Ring Music TheoryEpityllian
Scale 495Scale 495: Bocryllic, Ian Ring Music TheoryBocryllic
Scale 1519Scale 1519: Locrian/Aeolian Mixed, Ian Ring Music TheoryLocrian/Aeolian Mixed

This scale analysis was created by Ian Ring, Canadian Composer of works for Piano, and total music theory nerd. Scale notation generated by VexFlow, graph visualization by Graphviz, and MIDI playback by MIDI.js. Some scale names used on this and other pages are ©2005 William Zeitler (http://allthescales.org) used with permission.

Pitch spelling algorithm employed here is adapted from a method by Uzay Bora, Baris Tekin Tezel, and Alper Vahaplar. (An algorithm for spelling the pitches of any musical scale) Contact authors Patent owner: Dokuz Eylül University, Used with Permission. Contact TTO

Tons of background resources contributed to the production of this summary; for a list of these peruse this Bibliography. Special thanks to Richard Repp for helping with technical accuracy.